uniform circular motion of the crank-shaft. The degree of eccentricity or extent of throw given by an eccentric is equal to twice the distance between its centres of formation and revolution, and when practicability will admit, equal to the travel of the valve. 54. When the throw of eccentric and travel of valve are unequal, so as to cause a weigh-shaft and intervention of levers, how are the various lengths of levers obtained? For eccentric lever, multiply the throw of eccentric by length of valve lever, and divide by travel of valve. For valve lever, multiply the travel of valve by eccentric lever, and divide by throw of eccentric. Thus, suppose the throw of an eccentric equal 4 inches, travel of valve 8 inches, lever on weightshaft, to which valve-spindle is attached, twelve inches. 4 x 1286 inches, length of lever for eccentric rod. Úr 8 x64 = 12 inches, length of lever for valve-spindle. 55. If any doubt exist relative to an eccentric rod being of an improper length, when in its working situation on the engine, how is its accuracy or inaccuracy to be tested? Place and secure the valve at half-stroke by means of the packing or otherwise, bring the eccentric round upon the shaft to either extremity of throw, mark upon the rod the centre or diameter of the stud in the weigh-shaft lever, turn the eccentric round to the other extremity, and mark the stud upon the rod there also. If the receptacle in the rod for the stud be immediately equidistant, the rod is of a proper length; but if not, the rod must be lengthened or shortened equal to half the deviation observed. 56. It is essentially necessary, no doubt, that the various rods in a steam-engine, by which to communicate motion from one point to another, be in length to the greatest degree of exactitude; how are the dimensions of length for the principal rods thus to be determined? The proper length for the connecting-rod of a beam-engine, is the perpendicular distance be tween the centre of the beam and centre of flywheel shaft. The proper length for the side-rods of a leverengine, is the perpendicular distance between the centre of lever and centre of piston cross-head at half-stroke. The proper length for connecting-rods of directaction engines, is the distance between the centre of crank-axle and centre of piston cross-head at half-stroke. The proper length for an eccentric-rod, is the distance between the centre of fly-wheel shaft, or centre of revolution, and centre of stud in traverse shaft, when the valve is at half-stroke. 57. In speaking of an engine where the motion of the piston is communicated by means of a beam vibrating upon an axis, or by side-levers similarly actuated, what is to be understood when stated that the centre of the cylinder must be set half the versed sine in toward the centre of the beam? By versed sine is meant the difference between a straight line and that of a curved line, described by the centre of the stud in the end of the beam when moved through the whole stroke; hence the centre of the cylinder must coincide with half the distance between the chord and its arc as described by the beam. 58. Knowing the radius of the beam and the length of stroke, how is the versed sine to be ascer tained? The versed sine is the difference between the base and hypotenuse of a triangle, the hypotenuse being the radius of the beam, and the perpendicular of the triangle half the length of stroke; hence the rule: To the radius of the beam add half the length of stroke, multiply the sum by their difference, and the square root of the product subtracted. from the radius of the beam, equal the versed sine. Thus, suppose an engine with an equal-ended beam 14 feet in length, and the stroke of the piston five feet, what is the versed sine? 7+2.5 9.5 and 7—2.5=4.5: then √9.5×4.5 = 6.53 and 7-6.53.5 of a foot, the versed sine. 59. But how is it to be ascertained what portion of a foot the above remainder is, in our common mode of measurement by inches, or twelfths of a foot? Multiply the decimal by 12, and the whole number, if any, is inches; and again multiply the remaining decimals by 8, the whole number, if any, is eighths, &c. 60. How is the parallel motion in an engine, with regard to accuracy or inaccuracy, to be tested and adjusted? At half-stroke, if the piston-rod remain freely by the motion's guidance in the centre of the cylinder, and at the same time the parallel and radius bars parallel with the centre of the beam or side-levers, then may be concluded that they are each of a proper length, and that the radiusshaft or studs, as may be, are in their proper situations;―raise and lower the piston to the full extent of the stroke; and if, at both top and bottom, the cross-head is thrown outward from the centre of the cylinder, the stud in the beam or lever, which gives proper movement to the radiusbars, is too far out from the centre of the beam; but if, on the contrary, the cross-head be inclined toward the centre of the engine, then the stud is |